Skelhon scored 106.4 with his ten final shots as Frenchman Cedric Fevre broke the world and Paralympic record to take gold by three-tenths after both marksman had fired perfect rounds of 600 points in qualifying.
Recently shorn of his famous mohawk hair-cut which he wore in Beijing, Skelhon returned to the firing range just one day after failing to make the final in the standing air rifle event.
“I was over the moon with my qualifying," he said. "I've never seen eight guys shoot 600 before to get into the final.
“The final was awesome, all that noise and people cheering.
“I put in everything I had to get the gold, but my seventh shot, which I scored a 10.2, came back to haunt me.
“Getting a 10.2 is one of those things, it's part of shooting. I did everything I could."
However, there was disappointment for Di Coates. The veteran of eight Games with eight medals to her name finished 42nd in what could be her last Paralympics.
“My expectations were not what they were a couple of days ago,” said the 58-year-old who won her first Paralympic medals in 1984, the year Skelhon was born.
“I would have liked to be higher up the board than that. As to what I do now, I’m undecided. I’m going to go away and think about it.”
James Bevis, meanwhile, had won Great Britain's first London 2012 Paralympic shooting medal with a bronze in the 10m air rifle event.
Bevis just missed out on silver after a sudden death shoot-off with Frenchman Raphael Voltz but was delighted to improve on his 19th place finish in Beijing, especially after he just edged into the final as the eighth and final qualifier.
“I was really up for it, but in the end I’m relieved to be honest,” he said.
“Everything has gone to plan this week. I’ve been shooting world records in training and so when the pressure was on I knew I could do it.”